Aeroelastic load simulation of a 3 MW two bladed wind turbine

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Carsten Hansen

Aeroelastic load simulation of a 3 MW

two bladed wind turbine

27.05.2014

Masterarbeit eingereicht im Rahmen der Masterpr¨ufung im Studiengang Nachhaltige Energiesysteme im Maschinenbau am Department Maschinenbau und Produktion

der Fakult¨at Technik und Informatik

der Hochschule f¨ur Angewandte Wissenschaften Hamburg in Zusammenarbeit mit:

aerodyn engineering gmbh Hollerstraße 122

24782 B¨udelsdorf

Erstpr¨ufer: Prof. Peter Dalhoff Zweitp¨urferin: Frau Vera Schorbach

Industrieller Betreuer: Herr Jan-Christoph Hinrichs Abgabedatum: 27.05.2014

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Zusammenfassung / Abstract

Thema der Masterarbeit

Aeroelastischer Lastsimulation einer 3 MW Zweiblatt Windenergieanlage Stichworte

Wind, Lastsimulation, Pendelnabe, IEC 61400-1, Erm¨udung, Extrapolation Kurzzusammenfassung

Bisher war die Entwicklung moderner Windenergieanlagen fokusiert auf Anla-gen mit drei Blättern. Allerdings besitzen Zweiblattanlagen besonders für Off-shore Anwendungen einige Vorteile. Durch die Anwendung weiterer Methoden zur Lastreduktion könnten diese erheblich die Kosten für Strom aus Winden-ergie senken.

Ein vielversprechender Ansatz beinhaltet die Ausstattung einer Zweiblattanla-gen mit einer Pendelnabe, welche die BelastunZweiblattanla-gen f¨ur den Triebstrang enorm reduzieren kann. Das Potential einer Pendelnabe wird mit den Ergebnissen einer starren Anlage in dieser Arbeit verglichen. Dabei werden sowohl die Extrem-lasten als auch die Erm¨udungslasten nach der IEC 61400-1 Richtlinie bestimmt und verglichen.

Master Thesis Title

Aeroelastic load simulation of a 3 MW two bladed wind turbine Keywords

Wind, Load simulation, Teeter Hub, IEC 61400-1, Fatigue, Extrapolation Abstract

Previous development of modern wind turbines has been focused on three bladed turbines. However, two bladed turbines offer some advantages especially for offshore applications. By using additional methods for load reduction, these turbines could significantly reduce the cost of electricity from wind energy. A promising approach involves equipping the two bladed turbines with a teeter hub, which can reduce the strain on the drive train enormously. The potential of a teeter hub is compared with the loads of a rigid system in this thesis. Both the extreme loads and fatigue loads are determined and compared according to the IEC 61400-1 guideline.

Autor / Author

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Nomenclature

A Abnormal safety factor

AWT Adavanced wind turbine

BEM Blade element and momentum theory

CFD Computational fluid dynamics

D3 Delta-3 angle

deg degree

DLC Design load case

ECD Extreme coherent gust with direction change

ECG Extreme coherent gust

EDC Extreme direction change

Edition 2, ed2 IEC 61400-1 Edition 2 Edition 3, ed3 IEC 61400-1 Edition 3

EOG Extreme operating gust

Estop Emergency shut down

ETM Extreme turbulent model

EWM Extreme wind model

EWS Extreme wind shear model

FAST Fatigue, Aerodynamics, Structures and Turbulence

hor Horizontal

HSS High-speed shaft

IEC International Electrotechnical Comission

LSS Low-speed shaft

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min Minimum

N Normal safety factor

neg Negative

NREL National Renewable Energy Laboratory

Nstop Normal shut down

NTM Normal turbulence model

NWP Normal wind profile model

pos Positive

ra Rotor azimuth

SCD Super compact drive

SF Safety factor

T Transport safety factor

TI Turbulence intensity

TSR tip-speed-ratio

ver Vertical

WTGS Wind turbine generator system

yaw, y Yaw misalignment

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Symbols

Symbol Description Unit

a Axial flow induction factor [−]

a Slope parameter [−]

a0 Tangential flow induction factor [−]

k Skewness parameters [−]

k Component index (longitudinal, lateral, vertical) [−]

m Parameter for equivalent loads (4) [−]

n Number of cycles [−]

n Rotational speed s−1

nref Reference number of cycles (107) [−]

r Radius [m]

δr Radial size of blade element [m]

s Scale parameters [−]

t Time [s]

∆t Time difference [s]

u Location parameter [−]

vadd Additional wind speed caused by EWS [m/s]

vave Annual average wind speed [m/s]

vcg Size of coherent gust [m/s]

veN Extreme steady wind speed (N-year) [m/s]

vgust Amplitude of wind gust [m/s]

vhor Horizontal component of wind speed [m/s]

vhub Wind speed at hub height [m/s]

vin Cut-in wind speed [m/s]

vN Extreme turbulent wind speed (N-year) [m/s]

vout Cut-out wind speed [m/s]

vr Rated wind speed [m/s]

vref Reference wind speed [m/s]

vtot Total wind speed [m/s]

x Percentage change [%]

x Relative change [−]

y Yaw misalignment [deg]

yaw Yaw misalignment [deg]

z Height above ground [m]

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Symbol Description Unit

D Drag forces [N ]

D Rotor diameter [m]

F Force [N ]

F (x) Cumulative distribution function [−]

H Coherency decay constant [−]

I Moment of inertia kg m2

I15 Characteristic turbulence intensity at 15ms (Edition 2) [%] Iref Expected turbulence intensity at 15m_s (Edition 3) [%]

L Lift forces [N ]

L Load range [−]

Lc Coherency scale parameter [m]

Lk Integral scale (component index k) [m]

M Moment [N m]

MR Restoring moment of the teeter principle [N m]

P Power [W ]

Pe Probability of exceedance [−]

PR Probability according to Rayleigh distribution [−]

T Time, duration [s]

T Torque [N m]

T I Turbulence intensity [%]

Ud Wind speed in the rotor disc area [m/s]

Uw Wind speed in the wake area [m/s]

U∞ Incoming wind speed [m/s]

W Resultant relative velocity [m/s]

α Angle of attack [deg]

α Flow inclination [deg]

α Wind shear exponent / power law exponent [−]

β Blade set angle [deg]

∆β Pitch angle shift [deg]

γF Safety factor for loads [−]

δ3 Dela-3 angle [deg]

ζ Teeter angle [deg]

θcg Size of ECD direction change [deg]

θe Size of extreme direction change [deg]

σk Standard deviation of the wind velocity (component index k) [−]

φ Angle of relative velocity [deg]

Λ1 Turbulence scale parameter [m]

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Chapter 1

Introduction

1.1 Motivation

The main challenge of renewable energy systems is to achieve a low cost of energy in order to compete with conventional systems. Looking at the wind energy sector, three bladed turbines have been established successfully for the most onshore areas. Two bladed wind turbines could not match this development due to several onshore requirements. [1]

Two bladed turbines rotate faster and appear more disturbing to the eyes, whereas three bladed wind turbines seem calmer and therefore less disturb-ing in a landscape. But this disadvantage has no effect for offshore conditions. Due to the increasing number of offshore wind farms and increasing rotor sizes, new concepts for cost-efficient wind harvesting are considered. Therefore the two bladed turbines are brought back to discussion. [1, 2]

On the one hand, two bladed wind turbines are cheaper since they have one blade fewer and just a small decrease in aerodynamic efficiency. But on the other hand the dynamic loads caused by the wind shear and turbulence (figure 1.1) are higher. As a solution, different load reduction concepts are available for two bladed turbines, which can eliminate this disadvantage. [2, 1]

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CHAPTER 1. INTRODUCTION

Figure 1.1: Turbulent wind and teeter motion [3, page 215+224 modified]

A well known solution is to attach the rotor or the single rotor blades to a flexible structure with limited pivoting capability (figure 1.1). This can mini-mize the high bending moments which are the most significant structural loads. This teeter technology is only suitable for two bladed rotors and can have the potential to reduce the loads below any three bladed turbine. [4]

One additional important advantage of offshore applications is the handling of a two bladed rotor during transport and installation. The rotor or even the rotor including the nacelle of a two bladed turbine can be transported fully preassembled and pretested on a ship to a wind farm construction site. The final assemblies can be done on top of a installed tower in a single, time- and cost-saving operation. [4]

So the principal of a two bladed turbine has some encouraging opportunities to reduce the cost of energy. Especially the easy handling is for offshore ap-plications a big advantage. Further development and optimization of efficient turbine concepts should improve these benefits.

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1.2. SCOPE

1.2 Scope

The scope of this thesis is the load simulation of an existing wind turbine with a rigid hub and a modified teeter hub to reveal the load reduction potential. The simulation program which is used to calculate the loads and responses of the turbine is Bladed, which is developed by Garrad Hassan. An unvalidated simulation model of the turbine built in Bladed is the starting point of this thesis. As a reference for the model validation the simulation results of the turbine designer are used. These results are validated for the default turbine configuration with a rigid hub.

The goals of this thesis are:

Explanation of the teeter hub principals by reference to similar concepts of existing turbines.

Validation of the simulation model and the necessary adaptions to match the simulation results for the turbine with a rigid hub.

Definition of all design load cases according to IEC61400-1 edition 2 and 3 and a comparison of both editions.

Evaluation of the resulting extreme and fatigue loads and a comparison between the rigid and teeter hub.

The simulation results are focused on the hub and blade root loads. The loads on the tower, nacelle or single blade sections are not further considered. Other operating conditions are used to verify a correct operating mode.

This thesis will be published in the university library.

1.3 The Research Project

This thesis is part of the research project ZOFF at the University of Applied Sciences Hamburg. ZOFF (Zweiblatt-Offshore-Windenergie) is the abbreviation for two bladed offshore wind energy and works on concepts to reduce the cost of energy for offshore conditions. One main aspect of the ZOFF project is load simulation of two bladed turbines and the consequences on the turbine design, especially with the focus on turbines with a teeter hub. The handling of teeter end impacts appeared to be one of the key points for an efficient teetering concept. [5]

The company aerodyn engineering gmbh is a close partner to this project. It is one of the first companies, which was working on an overall development of wind turbines. The experience of 30 years in the development of complete wind turbines and all of their components is a great benefit for the project. aerodyn provides the information required for the project and data of the existing SCD 3.0 MW wind turbine with a rigid hub. A part of the project is to perform a

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CHAPTER 1. INTRODUCTION

feasibility study to use the same turbine structure with a teeter hub to minimize the dynamic loads. The turbine belongs to the super compact drive (SCD) series. The rotor bearing, the gear box, the generator and the yaw system are in a single very compact housing. [6]

aerodyn uses aeroFlex for load calculations and turbine development. This pro-gram is a result of an in-house customization of the known simulation software FLEX5 which was developed at the Technical University of Denmark by Stig Øye. The simulation data of the default turbine is available for the project and is used for the validation of the Bladed model as a reference.

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Chapter 2

Fundamentals

2.1 SCD 3.0 Turbine Info

The SCD 3.0 is the smallest turbine of the SCD series and developed by aerodyn engineering bmbh entirely. It is a two bladed upwind turbine with a rigid hub and a rotor diameter of 100 m. This type is designed for onshore conditions. Other kinds of the SCD series are two downwind offshore turbines, also with a two bladed rotor and a rated power of 6 and 8 MW. The picture below shows a part of a wind farm in China with four SCD 3.0 turbines.

Figure 2.1: Picture of the SCD 3.0 in a wind farm [6]

The existing hub belongs to the super compact drive series, with a really small hub. The nacelle has nearly the same diameter like the top of the tower and the blade roots. A drawing of the turbine head is shown in figure 2.2.

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CHAPTER 2. FUNDAMENTALS

Figure 2.2: Drawing of the turbine head [7]

The wind turbine generator system (WTGS) class and important turbine data is listed in table 2.1. There is already a newer version of the SCD 3.0 with a 110 m rotor diameter released by aerodyn, but this thesis in hand is researching the version with a 100 m rotor diameter.

Table 2.1: SCD 3.0 turbine data [6]

Geometry Wind Speeds

Type Horizontal axis Mean wind speed 8.5 m/s

WTGS class IIA (TC2A+) Cut in wind speed* 3 m/s

Rotor 2 blade upwind Rated wind speed 12.9 m/s

Rotor diameter 100 m Cut out wind speed 25 m/s

Hub height 85 m Diverse Parameter

Tilt angle 5 deg Wind shear gradient 0.2

Drive Train Mean yaw error 8 deg

Power limitation Pitch control Flow inclination 8 deg Operational mode Variable speed Air density 1.225 kg/m³

Rated power 3 MW Mean temperature 15 deg C

Rated rotor speed 17.1 rpm Generator

Converter system Full converter Permanent magnet synchronous * Cut in wind speed is 4 m/s for the simulations,

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2.2. TEETER HUB CONCEPTS

2.2 Teeter Hub Concepts

2.2.1 Teeter Principle

The main purpose of a teeter hub is to mitigate the bending moments in the whole drive train mainly caused by unequal blade loads. The loads are formed by divergent wind conditions on the single blades trough turbulence or wind shear. By allowing the rotor to teeter, the bending moments are not transmitted into the drive train.

While the rotor is rotating a restoring moment MR, generated by the lateral components of the centrifugal force, is pushing the rotor back into the rotation plane or neutral position (see figure 2.3). This moment is depending on three parameters which are coupled by the following equation. [8, page 271]

MR= IΩ2ζ (2.1)

The three parameters have different influences on the restoring moment. 1. Rotor moment of inertia I: The moment of inertia also includes the

mass of the rotor. A heavy rotor is resulting in a bigger restoring moment. 2. Rotor speed Ω: An increasing rotational speed of the rotor is raising

the restoring moment with a quadratic ratio.

3. Teeter angle ζ: The restoring moment is also linearly dependent on the teeter angle.

A further reduction of the teeter motion can be generated by a rotation of the teeter hinge axis relative to the rotor. So the teeter axis is no longer perpendic-ular to the blade axes. As a result the blade pitch angles are influenced by the teeter angle. One blade is getting rotated in a positive direction and the other one in a negative direction. The method is called delta-3 coupling. The rotation angle of the hinge is named delta-3 angle (δ3). The principle is illustrated in figure 2.3. [8, page 271]

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M r r r r

r

Figure 2.3: Teeter geometry [8, page 272]

The correlation of the produced pitch shift ∆β and the teeter angle ζ is as followed. [8, page 272]

∆β = ζ tan δ3 (2.2)

As an example: if the delta-3 angle is 45 deg the caused pitch shift is matching exactly the teeter angle. A possible teeter angle of 2.5 deg would result in a positive blade shift of 2.5 deg for one blade and a negative blade shift of -2.5 deg for the other blade. The positive pitch angle would reduce the aerodynamic loads on the blade which is charged with a higher load. The total teeter movement would be scaled-down every time the rotor is moving out of it’s neutral position. This process would damp the whole teeter movement. [8, page 272]

A coupling of the teeter angle and the pitch angle is a promising method to reduce the teeter movement and also the resulting loads. There are more op-portunities to realize this kind of coupling. For instance with a mechanical link built into the hub or an individual pitch control which is managed by the controller.

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Describing one possible teeter concept the AWT-26 turbine built by FloWind Corporation is a good and simple example. The development of the advanced wind turbine (AWT) project started in 1990 and was used for extensive testing of power performance, loads, dynamics and noise. The AWT turbines were designed to change there configurations to many different concepts, including a rigid or teeter hub. The AWT-26 is a downwind stall turbine and the concept of teetering can be explained by this research turbine very well. [9]

Considering the cone angle of a downwind turbine (the angle between the blade axis and the rotor plane), the teeter axis has to be located outside the hub center. This is caused by the displacement of the center of gravity of the rotor into the cone direction. If there is a offset between the center of gravity and the teeter axis, the rotor would always drift away from the neutral position. As a result the teeter concept with an external teeter axis can be seen in the following picture.

Figure 2.4: Schematic of the AWT-26 hub [10, modified]

To allow the turbine to teeter, the low speed shaft has been extended to reach the center of gravity of the rotor. At the end of the shaft, the teeter bearing is mounted, which allows a free movement around the teeter axis. The whole rotor system is attached by the teeter pin to the shaft.

Limiting the maximal allowable teeter angle, to avoid tower contact with the blades, requires a teeter restraint. The restraint concept of the AWT-26 had been with two teeter damper which were solidly mounted to the hub, with the task to limit extreme teeter angles. During further investigations this concept obtained very intensive end impacts and resultant damper failures. As a further development multiple dampers and other restraint concepts got investigated. [10]

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One promising concept was a damper which was supported by a spring and activated trough a sliding motion. The final result construction is shown in the following picture with a cross section of the hub.

Figure 2.5: Schematic of the AWT-26 teeter restraint [10]

The gap between the low speed shaft and the teeter restraint allows the rotor to teeter absolutely free and without any restraint in a certain range. If the gap gets closed by an exceeding teeter angle, the damper system stops the movement of the rotor. The free teeter range of the AWT turbines could be adjusted up to ±10 deg by changing the position of the damper and thereby the distance between the shaft and the damper.

2.2.2 Current Teeter Concepts

Load reduction is a real important design factor for two bladed turbines and also a driver for the reduction of energy costs. The wide variety of different two bladed turbine concepts shows no best practice in the past and until today. In the 1980s the number of different concepts was based on several research programs to identify possible new options to build wind turbines. A few new two bladed turbines in the 1990s were developed with a rigid hub and had no special load reduction concepts. But newer turbines from 2000 until today showed again a high variety on different concepts. Especially the concept of a teeter hub seems promising. [1]

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Looking at actual teeter concepts which are developed after the year 2000 offers a set of three commercial wind turbines built by three different companies. They are in a small power class of 0.5 to 1 MW and are already running in different wind farms. The UK based company Condor Wind Energy Limited is developing a bigger offshore turbine with a teeter hub. A previously announced 5 MW turbine is now replaced by a 6 MW turbine, which is currently under development and will be launched soon [11].

Opposing these turbines to the SCD 3.0 turbine, the main information are listed in table 2.2. A more relevant parameter for teetering would be the rotor mass, but this information is only available for a few turbines, so the total head mass (rotor + nacelle) is included.

Table 2.2: Turbines with a teeter hub after 2000

Turbine Rated Power Diameter Head Mass Status Sources

Windflow 500 500 kW 33.2 m 13.7 t Commercial [12, 13] GEV HP 1MW 1 MW 62 m 65 t Commercial [14] Nordic N1000 1 MW 59 m 40 t Commercial [15] Condor 5MW 5 MW 120 m 266 t Replaced [4, 11] Condor 6MW 6 MW 125 m 256 t Pending [11] SCD 3.0 3 MW 100 m ≈108 t Case Study [6]

Comparing the data shows that the SCD 3.0 turbine stands between the es-tablished small ones and the new developed Condor wind turbine. The head mass of just above 100 t seems relatively small compared to the other turbines, although the increased weight of a possible teeter hub system is not considered yet.

The development of the Condor turbine versions reveals a positive trend. Al-though the rotor size and the power is increased, the head mass of the 6 MW version could have been reduced about 10 tons.

A comparison of further operating features is listed in the next table. The listed tip-speed-ratios (TSR) which are calculated out of tip-speed and incoming wind speed are determined for rated speed.

Table 2.3: Operating features of the turbines

Turbine Orientation Regulation Rotational Speed TSR Tilt Angle

Windflow 500 Upwind Pitch ≈49 rpm 6.2 n/a

GEV HP 1MW Upwind Pitch 23 rpm 5.0 n/a

Nordic N1000 Upwind Stall 23 rpm 4.4 n/a

Condor 5MW Upwind Yawing 20.2 rpm 10.6 7 deg

Condor 6MW Upwind Yawing 19.4 rpm 10.2 7 deg

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As a specific matter of fact, the Condor turbine uses active yawing to control the power. The other turbines use a conventional pitch regulated power control system or in case of the Nordic turbine an active stall principle. Controlling the power by active yawing has the positive effect that there is no need for a complicated pitch system and the hub construction can be focused on the teeter hinge.

Last thing to mention is that the SCD 3.0 turbine hast the lowest rated ro-tational speed and a medium TSR. The teetering concept benefits a lot of a high rotational speed. A low rotational speed can result in bigger teeter angles during operation and also in intensive end impacts.

The following table provides more information to the teeter concept of the single turbines.

Table 2.4: Teeter information of the turbines

Turbine Teeter Hinge Pitch Coupling Teeter Range Teeter Lock

Windflow 500 n/a Mechanical ±2.2 deg (free) n/a

GEV HP 1MW Elastic Damper Delta-3 n/a n/a

Nordic N1000 Elastomeric Damper none ±2 deg n/a

Condor 5MW Elastomeric none ±2...4 deg yes

Condor 6MW Elastomeric none ±2...4 deg yes

SCD 3.0 open open ±6 deg (total) yes

Two turbines have a pitch-teeter coupling. The small Windflow 500 turbine has a mechanical linked mechanism which shifts the pitch angle corresponding to the teeter angle. The GEV HP 1MW turbine from Vergnet has a built-in delta-3 angle with the same result of a depending shift of the pitch angle. All known teeter hinges are constructed with a elastomeric bearing. The reason for this is the small permanent movement during operating mode would wear a bearing made of steel tremendous. Teeter ranges of the investigated turbines do not exceed 4 deg. The planned teeter range of the SCD 3.0 turbine with ±6 deg is the biggest one.

Having a closer look at the GEV HP 1MW turbine reveals another unique feature of a two bladed turbine. The upwind part of the nacelle can be lowered to a service position on the ground without any need of a crane or something similar. As a result, maintenance and blade cleaning can be performed at ground level. This position also grants hurricane protection. A picture of this process can be seen in the following picture.[14]

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Figure 2.6: Vergnet lowering system [16]

The delta-3 feature of the Vergnet turbine is shown in the next picture. By rotating the teeter axis in the rotor plane, the teeter movement is linked to a shift of the pitch angle. According to the picture, the delta-3 angle has to be at least 60 deg, because the teeter axis is nearly coaxial with the blade axis. This would create relatively high pitch angle shifts.

Figure 2.7: Vergnet delta-3 hub [16]

Both Condor wind turbines supposed to have the same teeter concept. During normal operation and at a wind speed below rated the teetering movement is limited to about 2 degrees. At higher wind speeds near the cut-out wind speed of 25m_s the movement increases to its maximum of 4 deg. [11]

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The teeter hinge assembly is displayed in the following picture. It consists of a T-shaped low speed shaft with two double elastomeric teeters, which are connected to the hub. In parked conditions the rotor can be locked mechanically, although a teeter lock mechanism cannot be seen on figure 2.8.

Figure 2.8: Condor teeter hub [11]

A smaller prototype, on which the Condor turbines are based (Gamma 60), had shown a high reduction of the gyroscopic forces with a teeter hub. The Condor 5MW has just 20 % of yaw moments compared to an equivalent three bladed turbine. This reduction makes a power control by active yawing possible. Only two of the three installed yaw drive systems are used to control the turbine and one system provides as system redundancy. [11, 4]

2.3 Simulation Tools

2.3.1 Aeroelastic Simulation Tools

Bladed and aeroFlex belong to the group of aeroelastic simulation tools. There are a lot of other software tools to simulate wind turbines and also some open source projects. But most of them are not validated for a design and certification of wind turbines. One other noteworthy simulation tool is FAST (Fatigue, Aerodynamics, Structures and Turbulence) which is developed and continuously advanced by the U.S. National Renewable Energy Laboratory (NREL). It was evaluated by Germanischer Lloyd and contains many different code packages [17]. However, all the simulation tools are based on similar aeroelastic theories and basic models.

The definition of aeroelasticity is according to Oxford Dictionaries: The science of the interaction between aerodynamic forces and non-rigid structures.” [18]

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2.3. SIMULATION TOOLS

Due to the flexibility of the rotor blades and the tower of a turbine, the interac-tion of the aerodynamic forces and the resulting deformainterac-tion of the blades are important. To neglect these interactions would make a realistic load simulation of wind turbines difficult. The combination of structural mechanics and the aerodynamic can be simulated by different methods.

To gain the most exact aerodynamic simulations, the computational fluid dy-namics (CFD) would be the best solution. But considering the calculation speed and the efficiency to simulate a lot of different wind conditions for a single tur-bine, the CFD calculation is far too time-consuming. For a holistic view of a wind turbine and the appearing loads, there are other methods to gain suitable results faster. [2, page 162]

The established model to calculate the rotor aerodynamics is the combined blade element and momentum theory (BEM) . This model is based on the simple actuator disk model, which treats the rotor as a two-dimensional disk that simply extracts kinetic energy out of the wind. How this works and what happens to the energy is not further considered. The only parameter is the axial flow induction factor a (or inflow factor), which defines the wind speed in the rotor disc area Ud depending on the incoming wind speed U∞. [8, page 42-43]

Ud= (1 − a) U∞ (2.3)

The momentum theory is dealing with the change of momentum of the air that passes through the disc area. This change is caused by the pressure differ-ence across the actuator disc. As a result of the theory, the wake wind speed Uw can be described by the inflow factor. The wake is the region of the flow, that is downstream of the disc and reduced by speed and static pressure. [8, page 42-44]

Uw= (1 − 2a) U∞ (2.4)

A further development of the actuator disk model is the rotor disc theory, which deals with the extracted energy and how this can be converted into usable energy. One of the main features is the additional wake rotation. The air gets an angular momentum through the reaction torque of the rotor. So in the wake of the rotor disc the air has a velocity component tangential to the rotor plane and in an opposite direction of the rotation. The change of tangential velocity is defined by the tangential flow induction factor a0. Associated to the change of momentum in the wake, this energy is lost for any further energy extraction by the rotor. [8, page 46-47]

As a extension of all these models, the blade element theory works with single blade elements. Therefore the rotor disc is divided into span wise elements that are located at the radius r and have the length δr. Each element is assigned to an airfoil with constant two-dimensional aerodynamic characteristics. These resulting ring areas cause an axial and angular momentum to all the air that passes them, based on the rotor disc theory. One element is shown in the following picture. [8, page 59-60]

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Figure 2.9: Blade element section [8, page 60]

The performance coefficients of an element depend on the airfoil and the angle of attack. The lift and drag coefficients have to be specified for each airfoil and each angle of attack separately.

The velocity components are defined by the wind speed U∞, the flow factors (a and a0) and the rotational speed of the rotor Ω. The resultant relative velocity W at the blade section is the result of the following equation. [8, page 60]

W = q U2 ∞(1 − a) 2 + Ω2_r2_{(1 + a}0₎2 _(2.5) The angle of this relative velocity acts at an angle φ to the plane of rotation, but the angle of attack α depends also on the blade set angle β. All velocity components and angles are shown in the following figure.

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With these information (the angle of attack, the velocity speed and the airfoil characteristics) the lift forces L and drag forces D can be determined for each element. The integration of all elements would reveal the total forces of the rotor and the generator torque.

The combination of these simple calculation models is a simple way to determine the resulting forces. As a further improvement the calculation can be extended with empirical parameters. For example simple factors to handle the tip and hub losses. These factors are added to the equations depending on the current wind conditions. [19, page 8]

Structural dynamics, on which the resulting forces have an effect on, can be simulated by two basic approaches. The finite element approach and the modal approach, which are considered as the most reliable methods of dynamic anal-ysis.

The traditional finite element approach is working with rigid bodies that are interconnected. The relative motion between these structural components is coupled to reaction forces with mathematical equations. A basic equation con-tains a stiffness matrix, a damping matrix and a mass matrix. [2] The simple coupling of two rigid bodies is shown in figure 2.11. Due to the flexibility of sev-eral turbine components, this method alone can not produce sufficient results.

Figure 2.11: Coupled bodies [2]

Wind turbine models involve mostly an additional modal approach to model the flexible components, especially the blades and the tower. The deformation of the flexible bodies is represented by a combination of several pre-calculated mode shape functions, which represent the strains and degrees of freedom of the component. The mode shape functions are calculated by standard linear finite element techniques. Therefore the components are reduced to single linear space beams, with two nodes located at the end and a defined mass and stiffness. [19, page 14-16]

The combination of these models can be called multi-body dynamics approach. The idea of connecting several rigid and dynamic bodies via nodes is displayed in figure 2.12 for a three bladed turbine.

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Figure 2.12: Multi-body dynamics nodes [20]

The combination of the BEM to simulate aerodynamic reactions and the two merged structural dynamic models reveals a really efficient way to simulate a full wind turbine. Although there are much more additional models that are involved to achieve sufficient results, the core concept is settled on these methods.

The abstractions which were applied make a fast turbine simulation possible by simultaneously gaining suitable results. More accurate simulations would slow down the whole development process at the present.

2.3.2 Comparing Bladed with aeroFlex

In this section the important differences between Bladed and aeroFlex are de-scribed. The focus is on the variations which are important for this thesis. With reference to the applied simulation models, Bladed is working with a com-bination of the finite element approach and the modal approach, while aeroFlex is using the plain modal approach. The aerodynamic models are both based on the BEM method, with small differences in the further extensions. [19, 7]

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Aerodynamic Moment

Beside of the lift and drag coefficient Bladed is working with a pitching moment coefficient. These coefficient produces a moment at a fixed point in the airfoil, depending on the wind speed and angle of attack. For the most cases these moment gets opposed by a moment, coming up by the lift forces and the distance to the pitch axis. The resulting moment is nearly zero, to avoid too high pitching forces. These moments are not treated by aeroFlex, which can result in small differences in the pitching forces of the blades.

Coordinate Systems

The two simulation tools work with different coordinate systems. They are shown in the following two pictures.

(a) Bladed [21, page 4.32] (b) Aeroflex [7]

Figure 2.13: Hub coordinate systems

The shown coordinate systems are related to the hub coordinate systems, but the differences are the same for all used coordinate systems in the turbine. The x- and z-axes are switched and the y-axis is rotated about 180 deg. The differences are listed in the table below.

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Table 2.5: Differences in the coordinate systems Bladed aeroFlex

x-axis z-axis y-axis - y-axis z-axis x-axis

If loads are compared between these two simulation tools, the aeroFlex loads are always converted into the Bladed coordinate system.

In figure 2.14 the blade coordinate system in Bladed is shown. According to the hub coordinate system the aeroFlex coordinate system is rotated again in the same origin. The x- and z-axes are switched and the y-axis is directing in the opposite direction.

Figure 2.14: Bladed blade coordinate system [21, page 4.31]

Reference Wind Speed

There is a difference in defining the wind speed vref, which is is the reference wind speed for a simulation. It can be seen in static simulations, where the wind has no variation and just a flow inclination α. In Bladed, this wind speed is the total wind speed vtot and in aeroFlex it is just the horizontal component vhor of the total wind speed.

Bladed aeroflex

α

v

tot

=

v

ref

_v

tot

α

v

hor

= v

ref

v

hor

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The relations between these two speed is cos α = vhor vtot =

vaerof lex

vBladed . Comparing these two simulation tools means, that the regarded wind speeds differ with the factor cos α = cos 8° = 0.99.

This small difference is attended during the validation between Bladed and aeroFlex. In later simulations and results, this influence is neglected.

Rotor Power

In aeroFlex the rotor power can be displayed for each simulation. In Bladed this value has to be calculated manually.

Using the basic formula for the correlation of power P , torque T and rotational speed n:

P = 2 π T n (2.6)

The total torque of the rotor is the sum of the torque on the low-speed shaft (LSS) of the generator TLSS and the mechanical loss torque TLoss.

PRotor= 2 π (TLSS+ TLoss) nRotor (2.7)

The resulting power corresponds to the rotor power in aeroFlex.

Speed-Torque Table and Losses

The speed-torque-table is one of the main controller features. It controls the generator torque depending on the actual generator speed. The two simulation tools have a different implementation of this look-up table.

By defining the speed and torque, the current power level is stated. The speed-torque-table controls the power at the section, where the controller is imple-mented. This point differs in the two simulation tools. The difference is shown in the following figure.

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CHAPTER 2. FUNDAMENTALS Controller Rotor Power HSS Power Generator Power Gearbox Generator Transformer etc. Electrical Power Electrical Losses 2 Mechanical Losses Electrical Losses Controller Mechanical Losses Electrical Losses Wind Bladed Aeroflex

Figure 2.16: Speed-torque table implementation

The Bladed speed-torque-table is connected to the high-speed shaft (HSS) power. This power is only decreased by the mechanical losses referred to the rotor power.

The aeroFlex controller is setting the torque of the generator, which is decreased additionally by the electrical losses in the generator. So this power level is lower than on the HSS.

An additional difference is that Aeroflex has two different steps for the electrical losses, while Bladed has one step for electrical losses. To avoid multiple different power levels, the comparison between these two simulation tools is reduced to the rotor power and resulting rotor speed curves. The electrical power and the annual energy yield will not be evaluated as a consequence.

2.4 IEC Guideline 61400-1

The International Electrotechnical Comission (IEC) has published a list of stan-dardization guidelines for wind turbines. They are listed under IEC 61400 with the general title “Wind turbines generator systems”. These standards are the theoretical groundwork for the development of wind turbines all over the world and other guidelines and standards are based on them[3, page 193]. One part of this work in hand is to compare the two newest versions of the the first part, called IEC 61400-1.

1. IEC 61400-1 Edition 2 from 1999 [22] 2. IEC 61400-1 Edition 3 from 2005 [23]

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2.4. IEC GUIDELINE 61400-1

The purpose of the part 1 is to outline a minimum of design requirements for wind turbines. The procedure and the arguments can be modified, if the safety of the wind turbine system is not compromised. So the usage of the guideline is really site and turbine specific.

A big part of the requirements treat the generation of different design situations, to predict all possible loads, that can occur in the turbine life time. Therefore a range of normal and extreme external conditions are defined, where the main focus lies on the definition of wind conditions. Other external conditions like salinity, lightning and earthquakes can be added if they can be expected for the turbine.

These external conditions are combined with design situations to different design load cases (DLC). A DLC can be for example the normal power production or the start up and shut down of the turbine. These design load cases have to be arranged and simulated for each turbine individually. Possible fault situations can be excluded, for example if the turbine manufacturer can prove a redundant safety system.

Changes in Edition 3

The title of the guidelines was changed from “Safety requirements” in the second edition to “Design requirements” in the third edition. This should reflect, that the focus is on a safe design rather than requirements for safety of personal. A lot of requirements were simplified to reduce the variety of opportunities. For example the gust models are reduced from a 50- and 1-year gust to one remaining gust and the partial safety factors and the requirements for the control and protection system have been adjusted.

But the most important changes are the expansion of the turbulence models and the extreme load extrapolation. These significant renewals are discussed in the following.

While the second edition was working with more steady wind conditions based on the normal wind profile model (NWP), the third edition requires more tur-bulent wind conditions for the load cases.

As an additional extension a new turbulence model was added, which is called extreme turbulent model (ETM). It is working like the normal turbulence model (NTM) but with a much higher turbulence intensity. A higher turbulence in-tensity results a more intense variation of wind speed and this will produce high extreme loads. The differences between the both turbulence models depending on the wind speed on hub height is shown in the following diagram.

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Figure 2.17: Comparison of the NTM and ETM

The rearrangement of the DLC is based on changing some wind models to the NTM and adding the ETM. Changes of the single DLC groups are:

DLC1.x Power Production: Six load cases from the second edition which were simulated with the NWP got reduced to two remaining cases. In addition the ETM is applied to simulate up to cut-out wind speed. DLC2.x Power Production with fault: Fault situations of the

con-trol and protection systems are now simulated with the NTM, which was previously simulated with the NWP in the second edition.

DLC3.x and DLC4.x: The setup of the NWP didn’t change for the start up and the normal shut down situations. Just the parameters for the condition changes (e.g. gust) are calculated with different parameters. The sizes of the gust models in edition 3 are also reduced in general. A comparison is made in appendix A.

DLC5.x Emergency Shut Down: Simulations of a emergency shut down are now changed from NWP to the NTM.

DLC6.x and DLC7.x: Parked and idling situations are mainly simu-lated with high wind speeds, according to the extreme wind model (EWM). The second edition was working with just a steady EWM model, where the third edition has now a steady and a turbulent EWM model.

Most striking is the changing to the NTM for extreme situations (Fault sit-uations, emergency stop and extreme wind for parked situations). Turbulent wind is always a random result of a calculation and can have a big influence on the resulting loads. A advice to handle these problem is not included in the guideline. Best practice would be a simulation of each load case with multiple wind files, but this would multiply the simulation effort.

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2.5. FATIGUE LOADS AND RAINFLOW COUNTING

One other major expansion of the third edition is the statistical extrapolation of extreme loads and events. The attempt is to find long term extreme loads by a set of short time simulations. Due to the turbulence issue, that random wind produces random loads, the extreme loads with a 50-year recurrence period is hard to detect. In the past, the safety factors were used to cover these loads. More information and how this extrapolation should work can be found in section 2.6 on page 28.

In conclusion, the third IEC edition is more lean and modern than the second edition. The increased simulation effort for turbulent wind conditions and sta-tistical extrapolation methods can be absorbed by newer computing power. The turbulent and extreme turbulent simulations will gain more realistic loads, than steady simulations with simple transient changes in wind conditions.

2.5 Fatigue Loads and Rainflow Counting

Determining the lifetime fatigue loads is an important design consideration for a wind turbine. Fatigue loads depend on the occurring load cycles during the lifetime of a turbine mainly. Therefore the expected amount and size of all appearing load cycles has to be determined.

As a first step, the expected distribution of different wind conditions and op-erating conditions has to be scheduled. A set of load cases is proposed by the IEC guidelines. The following situations belong to this set:

Normal power production

Power production with possible faults Start up

Normal shut down Parked

All this cases together will cover most of the situations, that will occur in a lifetime of a turbine. According to the WTGS class of the turbine and site specific conditions, these load cases are simulated for different wind speeds. The Rayleigh distribution is used to define the expected time period of each wind speed.

With this information and the simulation results, the appearing load cycles can be counted in each time series and then extrapolated to the total lifetime. The counting of load cycles can be done by different counting methods, but the rainflow counting is the most established method in wind turbine simulation. [24]

Therefore, the load time series have to be fragmented into single load hystereses. This is done by rotating the time axis in a vertical position and the load curve can be seen as a pagoda roof (the original name of the method was “Pagoda Roof Method”). Water drops are released at each extreme load and running down the roof. The procedure is shown in the figures below.

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(a) Simulated time series [24, page 18] (b) Rainflow counting procedure [24, page 19]

Figure 2.18: Rainflow counting method

After sorting and merging related downfalls, a set of different hystereses can be created. Dividing them into different groups of cycle ranges makes a counting possible. The result is a load histogram, which shows how many cycles of a specific cycle range is contained in the analyzed time series.

With the information of how often a specific time series is contained in the total life time of a turbine, the number of cycles get multiplied by a corresponding factor. The final combining of all load cases and cycles contains the total fatigue load.

For the consideration of the final fatigue loads, these histograms are converted to a load spectrum. These load spectrum will provide the cumulative cycle number of how often a specific load value is exceeded during lifetime. An example for two different load spectra is shown in the following figure.

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2.5. FATIGUE LOADS AND RAINFLOW COUNTING

Figure 2.19: Cumulative loads cycles by exceedance

The resulting load spectra have different appearances. To make a comparison more simple, they can be converted into a damage equivalent load. Therefore each step i of the load spectrum is considered with his number of cycles niand his load range Li. As a result of the following formula, the load spectrum has only one equivalent load LEquivalentleft for a specific number of cycles nref [19, p. 105]. LEqivalent= P (niLim) nref 1/m (2.8)

Especially the parameter m is depending on the material and geometry of the considered components. The parameters m and nref are therefore adopted from the designer of the turbine, to guarantee comparable results.

m = 4 nref = 107

For the first example in figure 2.19 the damage equivalent loads are shown in the following figure. Each load spectrum is reduced to one load step with a fixed cycle number of nref and a corresponding cycle range. In all later diagrams, the dashed lines are missed out and just the corner points and the info box will be shown.

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Figure 2.20: Damage equivalent loads

2.6 Statistical Extrapolation

One major renewal in the third edition of the IEC guideline is the statistical extrapolation of loads. It takes the results of the DLC1.1 simulations as a statistical basis, to predict the extreme loads for a specific time period. This new procedure is based on statistical methods mainly. [23, page 78-80]

Considering that the simulated wind files are created by a random process and cover a time period of 10 minutes, the detection of a 50-year extreme load seems impossible. The extrapolation method is assuming that the extreme loads occur at widely separated times and are statistically independent. As a result the simulated load maximums can be fitted to a probability distribution function. The long term exceedance probability will be able to be extrapolated for different time intervals.

To extract extreme values of the simulated loads, the guideline advises to select the largest value between successive upcrossings of the mean plus 1.4 times the standard deviation of the load process. The number and size of these extreme events can be counted, so that a probability for the exceedance of a specific load can be calculated. Based on all included simulations, a statistical distribution can be fit to these extreme events.

It is important to provide a sufficient number of simulation data over the range of significant wind conditions. There are different recommendations of how many simulation data is needed for each bin.

IEC Guideline (version 2005): “A minimum of 300 min of time series data distributed over the range of significant wind conditions is recommended.” [23, page 79]

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2.6. STATISTICAL EXTRAPOLATION

Bladed User Manual: “It is recommended that for a satisfactory distri-bution fitting, at least 50 simulations are carried out for each external conditions bin. For onshore calculations each simulation is usually 10 minutes long, ...” [25, page 139]

Bladed Theory Manual: “As a minimum the IEC 61400-1 Edition 3 stan-dard states that 15 simulations are necessary for each wind speed bin from (Vrated – 2m/s) to cut out and six simulations are necessary for each wind speed bin below (Vrated – 2m/s) ...” [19, page 109]

Because there is no specific number of necessary simulation time, the single results have to be checked for plausibility. A built-in verification method is implemented in Bladed, but further checks are recommended.

In Bladed there are two probability functions implemented for the fitting of the extreme data. According to the Bladed theory manual [19, page 108-110] the (2-parameter) Gumbel distribution and the 3-parameter Weibull distribution are the most applicable distributions to wind turbine loading. The following equations are the cumulative distribution function form of them.

Gumbel: F (x) = e−e −(x−u_s ) (2.9) 3-parameter Weibull: F (x) = 1 − e−(x−us ) k (2.10) The parameters are:

u = location parameter s = scale parameter k = skewness parameter

Because of the additional parameter on the 3-parameterWeibull function, this distribution is more flexible for fitting. But for some distributions, the Gumbel function fits better. This depends on the shape of the simulated distribution curve. This has to be decided case-by-case by comparing the resulting curves. To find the set of these parameters the method of least squares is used. This method tries to minimize the sum of the squares of the errors between the simulated data and the probability function. These errors can be influenced by different weighting factors. This should ensure, that enough contribution is given to the greatest extreme loads. The default weighting factors used in Bladed are displayed in the following table. The observed maximums a sorted by size and divided into groups. The biggest 5 percent of the maximums are weighted the most.

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Table 2.6: Weighting factors for the method of least squares [25] Range of Maximums Weighting Factor

0 to 80 % 0.01

80 to 95 % 1

95 to 100 % 10

After finding the best distribution function depending on the weighting factors the resulting tail of the function is used to extrapolate the loads. The following figure shows how the 50-year extreme load F50is determined from the computed long-term exceedance probability for four different fitting methods.

Figure 2.21: Example for an exceedance probability function [26, page 15]

The extrapolated loads are detected by their corresponding exceedance proba-bility. Both of the fitting methods implemented in Bladed reveal medium loads compared to the other fitting methods.

The exceedance probability is Pe(F50) = 3.8·10−7for a 50-year recurrence period and a reference period of 10 min. This value is the inverse of the amount of 10 minute intervals in 50 years (or simple 10min_50a ). According to this, the exceedance probability for a 1-year recurrence period is Pe(F1) = 1.9 · 10−5. With this probability value, the loads can be taken out of the diagram graphically. These two exceedance probabilities are demanded by the IEC guideline.

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2.6. STATISTICAL EXTRAPOLATION

The extrapolation is a challenge and requires significant effort to result in re-alistic and trustworthy results. In a case study of four state-of-the-art multi-megawatt turbines with different configurations some conclusions were drawn. Some of them are listed below. [27]

Comparing different fitting methods the log-normal and 3-parameter Weibull functions provide the most reliable results. Other fitting methods like gen-eral extreme value and Gumbel may lead to too conservative results. Trying to introduce non-linearity to the data distribution with the purpose

of tail fitting did not result in improved fits. This can lead to arbitrary loads.

To achieve realistic and reliable results, a significantly increased amount of simulation time and pre-/post-processing is required. The quality of the results has to be evaluated by visual inspection.

Even though the extrapolation method is mathematically correct, the vari-ability and interpretvari-ability of the results require a wide range of further analysis for any application case.

Based on these conclusions one final recommendation was made. The difficult execution of the load extrapolation should be replaced by other simplified meth-ods. Two possibilities also based on the DLC 1.1 results were tested. A scaling factor on the characteristic loads or a multiplier on the standard deviation can be used to determine the 50-year extreme loads. Although there was no clear tendencies of the factors and multipliers found in this paper, this approaches might be a more practical way to calculate extreme loads. [27]

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Chapter 3

Simulation Model

3.1 Control Scheme

External Controller

The external controller has been received from the turbine designer via an ex-ternal dll file. It should replace all Bladed inex-ternal control functions, so the behavior of the turbine is exactly the same as in aeroFlex. During the inte-gration to Bladed some problems occurred, because there are differences in the interpretation of such a dll file between the two simulation tools. Unfortunately, not all functions could get to run.

The normal power production is working fine with this external controller. But other control situations don’t perform very well with it (e.g. start up, shut down and fault situations). So these cases had been implemented by the Bladed internal controller with some losses in accuracy. But the missing controller functions would have optimized the different control situations and ignoring these functions would not result in lower loads. So the results of the simulations wont be scaled down by this issue.

Start Up Logic

The start up simulations start from a parked position with no rotor speed and the blades are pitched from 90 degrees down to the final pitch angle. The final pitch angle depends on the applied wind speed and will be defined in the load case description for each wind speed separately.

After reaching this final angle and a certain rotor speed, the external controller takes over control. The moment to put the generator on line, is the first point of the speed-torque table, that produces energy.

The implemented Bladed parameter for the internal controller are listed in ta-ble 3.1.

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3.1. CONTROL SCHEME

Table 3.1: Parameter for start up simulations

Parameter Value Unit

Initial Rotor Speed 0 rpm

Initial Pitch Angle 90 deg

Initial Pitch Rate -5 deg/s

Generator Speed to put on Line 270 rpm Final Pitch Angle 0...25 deg

Stop Logic

There are two different types of stops defined in the IEC guideline. The normal and the emergency stop. Both stops do have the same behavior. After triggering the stop, the turbine begins to pitch aiming at 90 degrees. After reaching a lower limit of rotor speed, the shaft brake gets initiated. The two modes just differ in the pitch rate and the cut in moment of the shaft brake (table 3.2).

At the beginning of the stop, the generator gets cut off the grid and stops producing power (like a grid loss). This is correct for an emergency stop, but should be prevented at a normal stop, because of the increasing rotor speed. After talking to the Bladed Support, there are no internal options for this prob-lem. Just a working external controller could solve this probprob-lem. An improvised method was applied, by triggering the safety system after a certain time. This will activate a pitch action, where the blades pitch with a defined pitch rate aiming at 90 deg. In this case, the generator moment follows the speed-torque table, until the rotor speed is too low for power production.

Another missing option is the final rotor azimuth angle. The rotor should be parked in a horizontally position, to avoid high loads caused by wind shear. This position can’t be guaranteed by the Bladed internal controller and is not further considered.

Table 3.2: Stop logic parameters

Normal Stop Emergency Stop

Pitch Rate [deg/s] 1 5

Final Pitch [deg] 90 90

Cut in of Shaft Brake [rpm] 1 6

Idling and Parked Conditions

The idling will not be applied by Aerodyn for this turbine to achieve a hurricane-proof operating mode. So this mode will not be further handled and simulated. The parked conditions are defined with a pitch angle of 90 degrees. The parked rotor azimuth angle should be, like for all two bladed wind turbines, 90 degrees. This will make sure, that the rotor is horizontally locked and the wind shear over height has no effect on it. The yaw angle will be 270 degrees from north (depending on wind direction) in normal parked conditions. All parameters are listed in table 3.3.

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CHAPTER 3. SIMULATION MODEL

Table 3.3: Parked parameters Parked Pitch angle [deg] 90 Rotor Azimuth [deg] 90

Yaw angle [deg] 270

Shaft Brake Characteristic

The shaft brake is mounted on the high speed shaft. It is working with hydraulic valves, so there is a maximum delay time of 0.5 seconds until the brake acts. It reaches the maximum braking torque of 59 kNm after an additional time of 0.4 seconds. The characteristic curve of the brake torque is described by the following formula.

TBrake(t) = Tmax− Tmax

1 + t T

e−Tt (3.1)

The time constant T was adjusted to 0.03 seconds, in order to reach the maxi-mum after the defined limit. The resulting time-torque curve which was imple-mented in Bladed is seen in figure 3.1.

Figure 3.1: Shaft brake characteristics

Safety and Control System

The safety system takes care about different fault situations and monitors the safety relevant turbine parameter. If any value exceeds the allowable ranges, the turbine shuts down automatically.

In the case of a grid loss, a brake chopper is used to consume the energy produced by the generator for a short amount of time, which is fed into the grid usually. So the generator torque stays alive for a short moment which allows the turbine to initiate to shut down progress. This prevents the rotor from overspeed. But this feature isn’t realized in the simulation model. During a grid loss, the generator torque is dropping to zero immediately.

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3.2. VALIDATION WITH AEROFLEX

While simulations with no defined faults, the safety systems is deactivated. In real conditions it is always activated, but while the simulations an unwanted shut down should be prevented. In the case of a fault, the setting of the safety system is described in the design load cases description in the appendix. In some cases, a stop is triggered manually by setting the stop time, because not all fault situations can be handled by the internal controller system.

3.2 Validation with aeroFlex

3.2.1 General Procedure

To validate the simulation model which was created in Bladed the simulation results in aeroFlex were taken as a basis. Measured data was not available for a further validation.

During the validation progress, the Bladed model was modified to achieve the same loads and operating parameters like the model in aeroFlex. The main focus was put on the hub and blade loads.

In the following sections the validation steps are described by means of the final model, which was the resulting output of the complete validation process.

3.2.2 Modal Analysis

As a first check the modal analysis can be taken to ensure a corresponding structural erection of the model. The blade and tower preferences are the most important parts of the simulation model. If the modal frequencies are different between the model in Bladed and aeroFlex, further simulations are pointless. Comparing the first two modal frequencies of the tower and the blades is suffi-cient to obtain certainty. They are listed in the next table.

Table 3.4: First modal frequencies Modal frequencies [Hz]

Tower aeroFlex Bladed

1. Tower 0.333 0.333

2. Tower 1.803 1.813

Blade aeroFlex Bladed

1. Flap wise 0.86 0.89

2. Flap wise 2.48 2.54

1. Edge wise 1.30 1.31

2. Edge wise 4.34 4.41

The minor differences in the frequencies point out a matching structural sim-ulation model of the tower and the blades. Further validation steps can be concentrated on the aerodynamic responses of the model.

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3.2.3 Steady Simulations

Comparing two simulation models should begin with a simple load case. In this case, it is a steady wind, with no yaw misalignment and no change in wind speed.

The selection of the magnitude of the wind speed is related to the wind speeds which are recommended by the IEC guideline. Two wind speeds which cover most of the relevant load situations are specified below.

0.8 vr is below rated and will provide a permanent pitch angle of 0 deg. This would ensure a matching pitch angle in both models.

1.2 vr is above rated. This would reveal the rated rotational speed and a possible pitch angle difference if the simulation models.

According to differences in the reference wind speed, the applied wind speeds in aeroFlex are increased and adjusted in Bladed.

This steady simulation is done with all influences listed below. Steady wind (no variation in wind speed)

Wind shear α = 0.2 Flow inclination α = 8 deg Mass and pitch imbalances

The relevant control variables that are important to check are listed in table 3.5. Only the mean values are listed. The deviation of the Bladed values are below 1 percent, except the pitch angle shows a small difference.

Table 3.5: Basic results for validation

Value Unit Aeroflex Bladed Aeroflex Bladed

Wind speed m/s 10.32 10.42 15.48 15.63

Rotor speed rpm 16.87 16.85 17.1 17.1

Generator speed rpm 402.7 402.3 408.2 408.2

Rotor Power kW 2199 2178 3523 3514

Pitch Angle deg 0 0 8.2 8.0

For the comparison of the resulting loads, a sample of the hub My load is shown below. The other load components have a similar appearance.

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Figure 3.2: Example of steady wind load response

These time series are reduced to the maximum and minimum values to make a comparison easier between the two simulation models. Also the aeroFlex loads were converted into the Bladed coordinate system to obtain uniform terms. The values in the following tables are calculated by the following formula, which returns the deviation of the Bladed results compared to the Aeroflex results in percent. x = 100 xBladed xaerof lex − 1 (3.2)

Table 3.6: Comparison of hub loads for steady wind conditions

Wind Speed

Load Min [%] Max [%] Min [%] Max [%] Mx -5.5 -0.3 -2.7 0.0 My 128.6 36.9 43.0 34.8 Mz -4.7 -6.0 -4.7 -3.9 Fx -4.6 -4.5 -4.8 -5.3 Fy 2.2 2.3 2.6 2.2 Fz 4.9 -1.3 4.8 -1.4 0.8 vr 1.2 vr

There is a huge difference for the hub My moment. All other loads have a deviation of 6 or less percent which would be a really good match.

The different hub My loads in Bladed and aeroFlex were treated by a lot of researches and couldn’t get solved. The fact, that all other values match very well is strange. Here is a short list of actions that were done, to solve this problem.

Deactivated a range of influences (mass and pitch imbalances, flow inclina-tion, tower shadow, stall hysteresis model) and varied the wind exponent, because this is the main source of loads for the hub My.

For small wind exponents, the loads match better, but the hub My is getting very low. For higher wind exponents, the hub My differs more.

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Assuming a different implementation of the wind shear model, the three wind components over the rotor area were compared. The differences in the definition of the reference wind speed led to this conclusion (??). But the components had no big differences, what would explain the high deviations.

Differences in the origin of the coordinate systems couldn’t get eliminated totally, but the R1-system in aeroFlex and the rotating-hub system in Bladed should be located in the intersection of the blade pitch axis. Because the hub loads are created out of the blade loads, the loads on the

blade roots were compared.

Looking at the blade root loads of the first blade shows similar results than the hub loads (table 3.7). All loads match with a maximal deviation of 10 percent, except the Mz loads. But the absolute values of the Mz loads are very low compared to the Mx and My loads, so a small deviation in this value would result in a high relative deviation to the aeroFlex model. Taking into account that aeroFlex isn’t calculating the aerodynamic moments of the airfoils the deviations can be ignored further. Apart from this, a blade Mz load would have no direct effect on the hub My loads. The hub My Loads are mainly created out of the blade My loads, which show a deviation of just 10 %.

Table 3.7: Comparison of root loads of blade 1

Wind Speed

Load Min [%] Max [%] Min [%] Max [%] Mx 3.1 -0.6 3.0 -0.2 My -9.9 -2.2 -7.3 -1.7 Mz -5.6 -19.1 -30.3 26.5 Fx -9.2 -3.0 -7.4 -2.8 Fy 0.4 0.8 1.5 -0.2 Fz 0.2 0.0 0.7 -0.3 0.8 vr 1.2 vr

Although there are differences in the hub My loads, the adjustment of the simulation model was finished at this point. The blade loads, which are mainly responsible for the hub loads, are nearly matching in both models. All other loads look good and it was decided to make a model freeze and to continue proceedings.

The comparison of a rigid and teetered hub can be done anyway. A possible mistake in the model would exist in both configurations and would not appear in a direct comparison.

3.2.4 Controller Check

After comparing the aerodynamic loads at steady wind conditions the imple-mentation of the controller dynamics has to be verified. The most important parameter managed by the controller is the rotor speed and the pitch angle.

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Step response

For a first check of the controller behavior and it’s time constants, a immediate rise in wind speed is applied and the resulting rotor speed and pitch angle are compared. There were three different wind speeds simulated with a rise of 5 m/s in speed. One time series is shown in the following figure and two other step responses are shown in the section C.1 on page 115.

Figure 3.3: Step response for controller validation

The behavior of the rotor speed and the pitch angles look really similar and the implementation of the controller dynamics should be fine. Just a small difference of the pitch angle is seen, similar to the pitch difference at steady wind conditions.

Rotor speed and pitch angles over wind speed

In the next diagram, the pitch angles and the rotor speed is shown for each wind speed. They were simulated by a normal power production with a linear rise of wind speed from 4 to 25 m/s in 900 seconds.

Aeroelastic load simulation of a 3 MW two bladed wind turbine

Carsten Hansen